By considering the new forms of notions lower semicontinuity, pseudomonotonicity, hemicontinuity and monotonicity considered scalar multiple integral functional, in this paper we study well-posedness a class variational problems with inequality constraints. More specifically, by defining set approximating solutions for under study, establish several results on well-posedness.

The paper is devoted to an analysis of optimality conditions for nonsmooth multidimensional problems the calculus variations with various types constraints, such as additional constraints at boundary and isoperimetric constraints. To derive conditions, we study generalised concepts differentiability functions called codifferentiability quasidifferentiability. Under some natural easily verifiabl...

In this paper, optimality conditions for the group sparse constrained optimization (GSCO) problems are studied. Firstly, equivalent characterizations of Bouligand tangent cone, Clarke cone and their corresponding normal cones set derived. Secondly, by using cones, four types stationary points GSCO given: TB-stationary point, NB-stationary TC-stationary point NC-stationary which used to characte...